i know that a linear combination of the vectors {v1,v2,...,vn} is any sum with terms that are scalar multiples of those vectors. But is a1v1 + a2v2 the same linear combination as a2v2 + a1v1? i know they evaluate to the same thing because vector addition is commutative but if i wanted to be precise would i say that it's the same linear combination or a different one only with the same set of coefficients? because if at least one of b1 and b2 was different from a1 and a2, then b1v1 + b2v2 is not considered to be the same linear combination even though they might be equal.(adsbygoogle = window.adsbygoogle || []).push({});

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# Precise definition of linear combination

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